This journal is©The Royal Society of Chemistry 2019 Mater. Horiz.

Cite this:DOI: 10.1039/c8mh01436a

Enhancing the electronic dimensionality of hybridorganic–inorganic frameworks by hydrogenbonded molecular cations†

Fedwa El-Mellouhi, *a Mohamed E. Madjet, a Golibjon R. Berdiyorov, a

El Tayeb Bentria,a Sergey N. Rashkeev, a Sabre Kais, b Akinlolu Akande, c

Carlo Motta, d Stefano Sanvito d and Fahhad H. Alharbi ae

Transition-metal oxides with pyroxene structure, such as alkali-

metal metavanadates, are known for their good chemical stability

and have been used accordingly in many applications. In this work,

we explore the possibility of enhancing the carrier transport and

optoelectronic properties of hybrid inorganic–organic metavanadates

MVO3 by introducing molecular cations. The hydrogen bonded

molecular cations are found to enhance the electronic effective

dimensionality of the system. This is related to the connectivity of

the atomic orbitals to form new electron and hole transport

channels. For the materials considered here, these channels are

formed by hydrogen bonding that, besides enhancing the stability,

results in enhanced macroscopic electronic transport and enhanced

photo-generated carriers relaxation time. Our study indicates that

the electronic dimensionality of the hybrid metavanadates could

exceed their subnanometer structural dimensionality which is a

desirable feature for improving their optoelectronic properties. This

concept can be generalized to a wider class of hybrid organic–

inorganic frameworks.

Hybrid framework materials development is a very fast growingfield in materials science because of its vast materials’ spaceand the fact that many compounds exhibit several technologicallyrelevant properties. One important group of hybrid materials ishybrid-halide perovskites with the composition ABX3, whereA = K+, Rb+, Cs+, MA+ (methylammonium), FA+ (formamidinium);B = Sn2+, Pb2+; and X = I�, Br�, Cl�. They recently attracted a greatdeal of interest because CH3NH3PbI3 (MAPI) and HC(NH2)2PbI3

(FAPI) show great performance in solar cell applications andmay be synthesized by straightforward chemical processingmethods.1–4 The solar conversion efficiency of single-junction

hybrid-halide perovskite devices exceeds 23.3%,1 a result probablyrelated to a unique combination of large absorption coefficientsand long carrier diffusion lengths resulting in low recombinationrates.5,6

However, it is well known that three dimensional (3D)CH3NH3PbI3 is structurally unstable and decomposes whenexposed to moisture, oxygen, and UV light.7,8 Therefore, thesearch of more stable and non-toxic materials for solar cell andoptoelectronic applications that exhibit high optical absorption,good charge carrier transport, and low recombination rate isstill a highly active field.

Vanadium-based oxide compounds have attracted a lot ofinterest in the past few decades due to their good electronic andoptical properties and their thermal stability. They have alreadyshown a great potential for practical applications as activeelectronic, optoelectronic, and catalytic materials.9 Solar-light-driven water oxidation is one of the areas where vanadates have

a Qatar Environment and Energy Research Institute, Hamad bin Khalifa University,

P. O. Box 34110, Doha, Qatar. E-mail: felmellouhi@hbku.edu.qab Department of Chemistry, Physics, and Birck Nanotechnology Center,

Purdue University, West Lafayette, Indiana 47907, USAc Department of Sciences, Institute of Technology, Ash Lane, Sligo, Irelandd School of Physics, AMBER and CRANN Institute, Trinity College, Dublin 2, Irelande College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8mh01436a

Received 11th November 2018,Accepted 28th February 2019

DOI: 10.1039/c8mh01436a

rsc.li/materials-horizons

Conceptual insightsWe demonstrate a new concept enabling the enhancement of carriertransport and optoelectronic properties of transition metal oxides byincorporating hydrogen bonded molecular cations. By means of a coherentand complementary state-of-the-art computational investigation supportedby comparison to experimental findings, we demonstrate that cationsforming hydrogen bonds with the inorganic framework can enhance theelectronic dimensionality of the system related to the connectivity of theatomic orbitals by forming new inter-channels electron and hole transportpathways. The present concept goes beyond the standard belief that thedimensionality of charge carrier transport is lower or equal to the structuraldimensionality (Mater. Horiz., 2017, 4, 206–216). We demonstrate that forhydrogen bonded hybrid materials the electronic dimensionality can exceedtheir structural dimensionality. As a result, the extraction of the photo-generated carriers is enhanced remarkably. The concept could begeneralized to the broader class of low dimensional Hybrid materials. Forexample, there are already strong indications that the long molecularbinders used to synthesize 2D/3D, 2D and 1D lead halide perovskitesmight play the role of carrier transport channels; this was highlightedbroadly without proof in a recent paper: J. Am. Chem. Soc., 2018, 140(23),7313–7323.

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already shown a great potential due to their suitable band gapsand a convenient band edge alignment with respect to waterredox levels.10–12 Vanadates are also considered as promisingelectrode materials in energy storage applications for large-scale high-performance metal-ion based batteries.13–19 This isdue to several advantages of these materials: they are cheap andsafe, easy to fabricate, having good thermal and environmentalstability, and capability of providing high energy density. Theself-activated and rare earth vanadates have also a promisingpotential for different lighting applications.20,21

Among the rich family of vanadate phosphors, metavanadatestructures MVO3 (M = K+, Rb+, and Cs+) are considered to begood candidates for the fabrication of light emitting deviceswith good light rendering properties and high quantumefficiency.22–24 Metavanadates can also be used as absorbingmaterials for solar cells applications25–28 due to their earth-abundant composition, easy fabrication, non-toxicity and, mostimportantly, exceptional chemical and thermal stability. More-over, the strong Coulomb interactions in some of the metavanadateswith Mott insulator behavior28 triggers multiple excitons generationper incident photon, which in turn increases their quantumefficiency.29,30 Importantly, the optoelectronic properties ofmetavanadates can also be refined by isovalent doping of theM-site elements.31–33 However, a full exploitation of vanadates’potentials require a fundamental understanding of their structuraland optoelectronic properties. Additionally, their transport propertiesrequire special attention, because of carrier trapping phenomenonand polaron formation processes.28

Using computer simulations we recently screened a set ofhybrid corner-sharing metavanadates MVO3, demonstratingthe possibility of reducing their optical band gap and, hence,boosting their optical absorption properties in the visible rangeof the solar spectrum.34 These materials are featured by onedimensional (1D) chains of connected (V5+O3

2�)� tetrahedraseparated by the M cations, suggesting the presence of 1Dchannel for carrier transport. Their crystalline structure is of abroad class of hybrid inorganic–organic frameworks in whichmulti-dentate organic molecules bind to multi-coordinatedmetal complexes (in this case, to the VO4 networks). Hence, theirsubsequent application as light harvesting materials suggests theneed for additional investigation of the carrier transport, mobilityestimation and cooling of hot photo-generated carriers.

The concept of electronic dimensionality was recently reported35

for describing the connectivity of the atomic orbitals in the lowerconduction band (CB) and the upper valence band (VB) due to theconnection of the corresponding atomic orbitals in metal-halideperovskites. It was concluded that high electronic dimensionality ismore desirable than the subnanometer structural one for achievinghigh photovoltaic performance. It was shown that as the structuraldimensionality of the prototypical Cs lead-iodine perovskitematerials reduces from 3D to 2D to 1D and 0D, there is anincrease in the anisotropy of the optical absorption coefficient.At the same time the charge carrier transport is reduced as thecharges get confined in lower dimensions. This demonstrates astrong correlation between the structural and the electronicdimensionally. Furthermore, lead-free compounds that appear

to have a 3D structural dimensionality at the subnanometerscale, such as prototype double perovskites Cs2AgBiBr6 sufferfrom a reduced 0D dimensionality of electronic transport causedby the lack of overlap between the Ag and Bi states at the relevantedge of the VB.

The interplay between the structural and electronic dimen-sionality is nowadays being exploited as a design strategy toovercome the stability and toxicity challenges in perovskitesolar cells.35 Recently, the quest for stable lead halide perovskitesresulted in lowering the 3D subnanometer dimensionalityrequirement in favour of 2D–3D perovskites materials.36 Despitetheir reduced power conversion efficiency (PCE), 2D–3D perovskitesare now considered as promising candidates for the deployment ofstable hybrid perovskite in the photovoltaic market. Similarly, thelimited number of non-toxic, earth abundant metal ions to designmaterials for solar applications is urging the community to start theexploration of materials beyond the 3D structural subnanometerdimensionality.37

In this work, we report the possibility of enhancing theelectronic dimensionality and the photo-generated carrier life-times of hybrid inorganic–organic metavanadates by introducingorganic cations into the inorganic framework. Nonetheless, theproposed technique is general and is applicable to a wide rangeof hybrid materials. Inorganic MVO3 pyroxenes metavanadatesusually display 1D chain connectivity, anisotropic absorptionfeatures and 1D chain anisotropic carrier transport.34 Here wecompare the charge transport properties of materials MVO3

(where M = Cs+, NH4+, and H3S+) by using density functional

theory combined with a nonequilibrium Green’s functionsapproach (DFT+NEGF) to charge transport. In addition, we havegone beyond the constant relaxation time approximation inusing the Boltzmann theory of transport by calculating explicitlythe carrier mobility and relaxation time (scattering time). Thiswas achieved by taking fully into account various scatteringmechanisms such as the impurity and electron–phonon scatterings.Furthermore, we have explored the impact of the electron–phononinteraction on the hot charge carrier cooling after photoexcitationusing nonadiabatic molecular dynamics simulations in combi-nation with time-domain DFT. All computational details can befound in the ESI.†

We found that molecular cations can be used to change theelectronic dimensionality of the system by forming extra trans-port channels related to the formation of hydrogen bondsbetween the hydrogenated molecular cation M+ and the VO4

network. The formation of these channels increases the electronicdimensionality of the material at the inter-atomic level or so-calledsubnanoscale and results in enhanced electronic transportproperties. Our findings indicate the possibility of improvingcarrier transport properties of hybrid materials by suitablecation replacement for practical applications.

A. Structural and electronic properties

Fig. 1 shows the optimized structures of the pyroxene metavanadatesMVO3, featuring 1D chains of VO4 tetrahedra linked by two

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corner oxygen atoms. The chains extend parallel to the c axis,and are separated by the cations M = Cs+, NH4

+, and H3S+,having effective ionic radii of 174, 144 and 200 pm respectively. Thehybrid metavanadates with M = NH4

+, H3S+ are characterised by thepresence of N–H� � �O and S–H� � �O hydrogen bond networks38

within the ab plane, as demonstrated in our earlier study.34 Thecalculations started from the experimental structures39 reported forthe CsVO3 and NH4VO3 followed by a full optimization of bothatomic positions and lattice parameters. We find that the fullyinorganic system CsVO3 (see Fig. 1(a)) has lattice parameters a =5.46 Å, b = 12.42 Å and c = 5.86 Å, values that are in agreement withthe experimental results39 (a = 5.39 Å, b = 12.25 Å and c = 5.78 Å).Our relaxed structure for NH4VO3 is also orthorhombic (Fig. 1(b)),with lattice parameters a = 4.88 Å, b = 11.99 Å and c = 5.91 Å whichare also comparable to experimental parameters39 (a = 4.91 Å,b = 11.78 Å and c = 5.83 Å). It is noticeable, as reported earlier,34

that the VO4 inter-chain distances within the ab plane are signifi-cantly reduced because of the smaller ionic radius of NH4

+ comparedto Cs+, in addition to the presence of the bridging N–H� � �O hydrogenbond network. The impact of this structural modification andhydrogen bond network on the optoelectronic and charge carriermobility will be discussed in the following sections.

In the case of the computationally designed hybrid meta-vanadate34 H3SVO3, the VO4 inter-chain distance along theb axis chain becomes larger than in the case of CsVO3 (a = 5.25 Å,b = 13.60 Å and c = 5.88 Å) while the inter-chain distance is reducedalong the a axis. This is partially due to the larger ionic radius ofH3S+ compared to Cs+ but also to its dipole moment of 1.83 Debyeand the directionality of the S–H� � �O hydrogen bond network.Consequences on the electronic transport and carrier mobility willbe discussed further in the next section.

The optical properties of the metavanadates have been discussedextensively in our previous work.34 Overall, the optical spectra of thesystems with organic cations show peak intensity comparable to theinorganic CsVO3 (see Fig. S4, ESI†). However, the H3SVO3 samplewith hydrogen bonds between cations and the inorganic framework

absorbs over a wider range of the solar spectrum due the bandgapreduction towards the visible sector. Interested readers might findfurther details in the ESI† and ref. 34.

In order to visualize the contribution of the M-site cations tothe electronic density of states (DOS), we have calculated theband structure and orbital projected density of states (PDOS) for allconsidered systems. For both MVO3 systems where M = Cs+ andNH4

+ [see Fig. S5 and S6 in the ESI†], the DOS of the system ismostly dominated by the p-states of the O atoms and the d-states ofV atoms, with minor contribution from the M cation. The valenceband edge (VBE) states that are relevant for carrier transport, aredominated by O, while the V dominates the CB edge, where stronghybridization of the p-states of O and d-states of V is observed. Nosignificant contribution of the M-site elements is observed for theconsidered energy range. A comparison between the band structureof materials with M = Cs+ and NH4

+ indicates that both havebandgaps of B3 eV and their bands are degenerated at the VBand CB edges. These bands are more dispersive for NH4

+ suggestingimproved carrier effective masses (see Table S1, ESI†). Interestingly,the situation changes considerably in the case of H3SVO3. Thiscompound has a band gap of 1.7 eV with the VB maximum (VBM)resulting from the hybridization of the p-states of O and those of S34

(see Fig. S7, ESI†), whereas the CB minimum (CBM) remainsdominated by the p-states of O and the d-states of V. This indicatessignificant spatial separation of possible photogenerated electron–hole pairs in the system, which may affect the lifetime of the chargecarriers. Because of the appearance of these new hybridized S and Ostates at the VBM, the band gap of H3SVO3 reduces considerably ascompared to the other compounds. In addition, the bands at the VBand CB edges are non-degenerate and less dispersed.

Note that spin–orbit coupling has a negligible effect on theelectronic properties of the systems considered as was shown inour previous work.34 In addition, higher level of theory such asHSE06 and G0W0 were taken into account in the same work tocorrect the PBE-DFT bandgap underestimation issue.34 Theincreased interchain distance along the b direction combinedwith the non-negligible distortion of the VO4 tetrahedra and thecrystal field splitting are responsible for lifting the bandsdegeneracy. This attempts to reduce the band gap of metava-nadates to the visible region by cation exchange, while success-ful in the case of M = H3S+, appears to affect considerably thecurvature of the bands and consequently the carrier effectivemasses. Nevertheless, under finite temperature operating conditions,an efficient collection of photogenerated charge carriers requires:(a) good electrical conductivity; (b) a long carrier scattering time orso-called relaxation time, and; (c) a long timescale of photoexcitedcarrier relaxation to the band edges to ensure their collection anddelay the radiative/non-radiative recombination.

B. Microscopic electronic transportproperties

In this section, we study the electronic transport properties ofthe materials under consideration by using the DFT+NEGFapproach (details of the approach used can be found in ESI†).

Fig. 1 Metavanadate pyroxene optimized crystal structures for: (a) CsVO3,(b) NH4VO3, and (c) H3SVO3. Red: VO4 polyhedra centred at V, purple: Cs,pink: H, blue: N, yellow: S. N–H� � �O and S–H� � �O hydrogen bond net-works are presented by dotted lines.

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We start by analysing the zero bias transmission spectra, T(E),which are shown in Fig. 2 as a function of the electronic energyfor all the considered samples. The transmission is calculatedalong the VO4 chains (parallel to c axis, see Fig. S2, ESI†) whilethe energy zero is set to be the Fermi level of the system. Thetransmission at the CB edge (CBE) for CsVO3 and NH4VO3 ischaracterized by a broad and doubly degenerate peaks [arrows(a and d)], with a transmission amplitude around T = 2.0. Thisindicates that both channels along the VO4 chains are activatedsimultaneously and become available for electronic transport.Interestingly, NH4VO3 exhibits a slight increase at the CB statetransmission as labelled by the arrows (b and e) giving indicationthat additional electron transmission channels might becomeavailable. Interestingly, the transmission at CBE for H3SVO3 ischaracterized by two distinct non-degenerate peaks shaved at anamplitude of 2.0 as indicated by the arrows c and f. The lifteddegeneracy in the transmission might originate from the lifteddegeneracy observed earlier in the electronic band structure. Itindicates that each VO4 chains channel might be activatedseparately in addition to existing channels of transport. TheVBE transmission spectrum for CsVO3 is characterized by awell pronounced peak with an amplitude exceeding 2.0, whileNH4VO3 has a wide multi-dented peak with a maximum reachingup to an amplitude of 3.0. The VBE transmission spectrum forH3SVO3 is a single peak extending up to energies (VBM-0.5 eV),with an amplitude of 1.0. Worth noting that the states at the VBEare hybridized S and O p-states as shown in the previous sectionin the PDOS and band structure analysis. Hence, despite thelifted degeneracy observed for the H3SVO3 transmission spec-trum, the material has the smallest zero-transmission area due toits smallest band gap. This means that upon application of a biasvoltage H3SVO3 will be the material for which the current on-setwill appear at the lowest voltage. We have calculated electrostaticpotential variations, which are also one of the important factorsaffecting the charge transport on the system. Fig. S3 (ESI†) showsthe averaged electrostatic difference potential for the consideredsystems along the transport direction. For both samples, weobtained periodic potential oscillations. However, both theamplitude and the frequency of the oscillations are larger in

the NH4VO3 sample (dashed red curve) as compared to theones in H3SVO3 system (solid black curve) suggesting that thescattering of the electrons from these potential oscillationsreduce their transport through the system. This being said,electrostatic potential is not the only mechanism limiting thecarrier scattering time because e-phonon interaction is alsoimportant as will be discussed in the next section.

Looking more closely at the microscopic transport, it isknown that localization of electronic states is one of the mainfactors affecting the electronic transmission. Fig. 3 shows theisosurface plots of the projected self-consistent Hamiltonianeigenstates (PSH) of all the considered materials for the peakedtransmissions that correspond to the CBM (a–c) and CBM + 1(d–f) states. In most systems, the visualized electronic trans-mission channels (Fig. 3a–f) extend along the two available VO4

chain channels. Interestingly, in the case of NH4VO3 andH3SVO3 hybrid metavanadates, the PSH are spread over themolecule as well, which means that the corresponding transportchannels are opened so that some electrons can pass throughthe interchain region perpendicular to the c axis. In fact, theelectronic states become extended within the VO4 interchainregion passing by the N–H� � �O and S–H� � �O hydrogen bondsexplaining the transmission values higher than 2.0 observed inFig. 2. This is even more evident from Fig. 3c and f for everyindividual VO4 channel. Additional channels across the VO4

chains are observed by visual inspection indicating the extra

Fig. 2 (top) Calculated zero bias transmission coefficients along the VO4

chains (parallel to c axis) as a function of electron energy for CsVO3,NH4VO3, and H3SVO3 samples. Arrows and labels (a–f) point to relevantelectron transmission channels at CBM and CBM + 1. The zero of energy isset to be the Fermi level of the given system.

Fig. 3 Zero bias isosurface plots (isovalues are �0.05 (cyan colour) and +0.05(magenta colour) Å�3/2) of the projected self-consistent Hamiltonian (PHS)eigenstates for the peaked transmissions that correspond to the conductionband minimum (CBM) (a–c) and CBM + 1 (d–f) states of the samples CsVO3

(a and d), NH3VO3 (b and e), and H3SVO3 (c and f).

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transmission channel opening due to the extended electronicstates between the VO4 channels. Such delocalization occursthrough the hydrogen bonded H3S molecule In fact, electronscoming from one metal electrode with continuous energy inter-action with electrons at molecular orbitals and then transportthrough the VO4 chains to the other electrode. If moleculesinteracting with the VO4 chains via hydrogen bonding arepresent, the orbital is delocalized across the molecule. Thus,an electron entering the material at the energy of the orbital hasa high probability of going through the molecule to reach theneighbouring VO4 channel and, hence, creating additionalchannels of transport.

We conclude that the devices made of metavanadates containinghydrogen bonds can exhibit additional transport channels thanthose made of materials without molecular cations since O atomsplay the role of electron donors while nitrogen and sulfur atoms areelectron acceptors. These additional channels of transport mightserve to spatially separate the e–h pair and help avoiding the rapidexciton recombination. The investigation done here indicates thatthe electronic dimensionality of the hybrid metavanadates mightexceed their subnanometer structural dimensionality, which isa desirable feature for enhancing compounds’ optoelectronicproperties.35

C. Macroscopic charge carrier mobilityand scattering time

In order to further elucidate the increased electronic dimensionalityobserved in the hybrid organic–inorganic metavanadates, weestimated the direction-dependent electrical conductivity of thethree samples by solving the Boltzmann transport equations(BTEs). Computational details can be found in the ESI.† At finitetemperature device operating temperature, the macroscopiccharge transport depends not only on the electrical conductivityof these materials but also on the carrier scattering mechanismssuch as interactions with phonons, inelastic scattering mechanisms,ionized impurities, piezoelectricity, deformation potential andcharged dislocations. These scattering mechanisms can besummated using Matthiessen’s rule for the elastic scatteringand the Fermi golden rule for phonon scattering to calculatethe carrier relaxation time (ts).

41 Although, it is common toemploy the constant relaxation time approximation (BTE-CRA)for a wide class of thermoelectric materials,40,41 our initialassessment demonstrated that this approach is not valid forthe pyroxene metavanadates. This is because of the largedifferences in the calculated polar optical phonon (PO) fre-quencies between CsVO3 and NH4VO3 (see Table S1, ESI†)raising the need to explicitly compute ts. Hence, we calculatethe k-dependent relaxation time, which is combined with theelectrical conductivity s/ts obtained from solving BTE and used toestimate the electron and hole mobility m = s/(ne), where n ischarge carrier concentration (in cm�3) and e is the electron charge.

An attempt was made before to calculate transport, using‘‘ab initio Model for mobility calculation using BoltzmannTransport equation’’ – the so called aMoBT model42 which fully

captures the elastic and inelastic scattering of charge carriersusing a single band model. Despite our highly accurate calculationof band structure, deformation potential, dielectric function, andoptical phonon frequency (see Table S1, ESI†), this approach didnot capture accurately the electron–phonon scattering that isdominant at high temperatures. This is due to inappropriatenessof the single band model to our metavanadates exhibiting bandstructure with multiple band degeneracy and band crossing (seeFig. S5–S7, ESI†). Nevertheless, it helped us confirm that scatteringmechanism such as ionized impurity do not dominate thecarrier scattering and could be neglected, strengthening theassumption that electron–phonon scattering is the most dominantmechanism.

The newly released BoltzTraP243 software package, besidesits enhanced electronic band fitting performance over Boltztrap,44

calculates a smoothed Fourier expression of periodic functionsand the Onsager transport coefficients using the linearized BTE. Ituses as input only the bands and k-dependent phonon energies, aswell as the intra-band optical matrix elements and scattering rates(if available).43 The scattering rate was computed by means ofAbinit package,45 with its robust implementation of electron–phonon interaction within density functional perturbation theory(DFPT).46

The electron phonon scattering has been fully accounted forby fulfilling the conservation of energy and k0 � k = q + g with g areciprocal lattice vector k, q are the grid of points in the BZ. Thefeature to calculate relaxation time for semiconductor case wasimplemented in anaddb routine (part of the Abinit package)only in 2016 and it requires large computational power.46

Calculation details are presented in the ESI.†The resulting calculated relaxation times from BoltzTraP243

are in the femtosecond range, namely, ts = 3.9 fs for CsVO3,85 fs for NH4VO3, and 20 fs for H3SVO3. The order of magnitudefor ts is comparable with the values reported earlier for efficientphotoabsorbers such as MAPI47 (ts = 10 fs) and CuSnSbS3

41

(ts = 40 fs). These calculated values provide a better representationof the thermoelectric properties, and give a strong indication oftransport properties for this class of materials.

Fig. 4 presents the hole and electron mobility m (in cm2 V�1 s�1)at 300 K averaged over all crystallographic directions for CsVO3,NH4VO3, and H3SVO3 as a function of the charge concentration r.The electron mobility averaged over all transport directionsof transport for the inorganic CsVO3 reaches a maximum

Fig. 4 Average hole and electron mobility m in (cm2 V�1 s�1) for CsVO3

(black), NH4VO3 (red) and H3SVO3 (blue) as a function of the chargeconcentration, r, calculated with k-dependent relaxation time.

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m = 16.5 cm2 V�1 s�1 due to its small relaxation time. Interestingly,NH4VO3 has an order of magnitude higher mobility m =130 cm2 V�1 s�1 while H3SVO3 has an intermediate value ofm = 50 cm2 V�1 s�1. The hole mobility for the inorganic CsVO3

reaches a maximum of m = 4.0 cm2 V�1 s�1, NH4VO3 has a twoorders of magnitude higher mobility of m = 130 cm2 V�1 s�1

while H3SVO3 had the lowest hole mobility, m = 1.3 cm2 V�1 s�1.It is impressive that hybrid metavanadate, NH4VO3 has com-parable average electron and hole mobilities, an advantageousfeature for the generation of current and charge extraction.

Comparing again the crystallographic and electronic dimen-sionalities, one notices from Fig. 5 and Fig. S8–S12 (ESI†) thatconductivity and mobility of metavanadates as function of thecharge concentration are anisotropic in all three directions xx,yy and zz. However, interesting electronic dimensionallyfeatures emerge for each of the considered material: CsVO3

has a high electron mobility along the zz direction (parallel tothe VO4 chains) reaching up to 106 cm2 V�1 s�1 and insignificantmobility along the directions perpendicular to the chains namelyxx and yy (see Fig. S9, ESI†). In contrast, it has low hole mobilityalong all crystallographic directions, a fact that can be attributed tothe single flat band lying at close to the VB, and the smallconductivity peak is observed in Fig. S8 (ESI†). This dominatesfor carrier concentration less than 3 � 1022 cm�1. Hence, CsVO3

has both a 1D structural and electronic dimensionality.The direction-dependant conductivity and mobility for

NH4VO3 are shown in Fig. 5. The electron mobility here is alsodominated by the zz component. However, a noticeable increaseby an order of magnitude in the mobility along yy is clearly seenfrom the insets of Fig. S10 (ESI†). Moving to the hole mobilities,a significant enhancement in the mobility along the xx directiondominates the hole transport where the zz direction motilitiesstart to raise only at carrier concentration higher than 3 �1022 cm�1. The direction dependent conductivity and mobilityassessment of NH4VO3 confirms our earlier finding usingDFT+NEGF about the opening of additional electronic channelsof transport along the xx and yy directions in the interchainregion which are absent in the case of the inorganic metavanadatepyroxene CsVO3. It also confirms the earlier claim about theactivation of channels along the N–H� � �O hydrogen bonds asadditional channel of transport, contributing to enhancing theelectronic dimensionality above 1D. Interestingly, NH4VO3 offersan interesting anisotropic scenario of long lived electron–hole pair

due to the spatial separation after photoexitation, with electronstransporting predominantly along the VO4 chains (zz direction)combined with hole transport along the xx direction.

H3SVO3 displays features similar to NH4VO3 (Fig. S11 and S12,ESI†): the electron transport is dominated by the zz component,and the activated channels of transport along xx and yy could beclearly seen as components confirming our earlier finding usingDFT+NEGF. The mobility along the xx and yy directions alsocontributes in making the averaged electron mobility higher thanthat of CsVO3. Here, we also witness an enhanced electronicdimensionality beyond 1D by the activation of the S–H� � �Ohydrogen bonds as additional channel of transport betweenVO4 chains. Unfortunately, this compound has a weak holemobility compared to the others. This low-hole mobility can beexplained by the one band contributing in the conductivity (seeband structure in Fig. S7, ESI†) which is also noticeable from themodest conductivity peak in Fig. S11 (ESI†).

The temperature dependent mobility is shown in Fig. S13(ESI†), demonstrating that both electron and hole mobilitydecreases with increasing temperature for all metavanadatecompounds. This is an expected behaviour due to the fact thatthe electron–phonon scattering mechanism dominates the totalrelaxation time term above room temperature. Nonetheless, thecompounds keep reasonably good mobilities at room temperaturesthat will be utilized in Section E to evaluate the carrier diffusioncoefficient and the diffusion lengths. Before we present our resultson these, the hot carrier lifetimes are computed and discussed,comparing two hybrid metavanadates, in the next section.

D. Photo-generated charge carrierrelaxation time

In the present study, the investigation of the cooling process ofhot electrons and hot holes is done separately. We consider theexcitation of electrons from the VBM to states in the CB withenergy DEe above the CBM. Then we investigate the relaxationdynamics of hot electrons from these states to the CBE. Tostudy the thermalization of hot holes, we promote electronsfrom states below the VBM with energy DEh. Since the electron–hole interaction is neglected in this approach, the relaxationoccurs due to the interaction between charge carriers of the sametype and the interaction of the charge carriers with phonons.More details about the computational methodology can be foundin the ESI.†

Fig. 6 shows the electron (top panel) and hole (bottom panel)population decay time from different initial excited state energiesDEe/DEh (above the CBM/below the VBM) for the three systems. Itis clear that the hot carrier decay process is faster in the case ofNH4VO3. For most of the excited state energies, the coolingprocess of hot-carriers in CsVO3 system is faster than the onein H3SVO3 and slower than the one in NH4VO3. The increase inthe hot electron relaxation time at 0.81 eV, which corresponds toCBM + 4 state as initially populated state, is mainly due to largerenergy gap between CBM + 4 and CBM + 3 states. Note that thisenergy gap is about 0.4 eV (see also Fig. 7) for CsVO3 which is

Fig. 5 Hole mobility and electron mobility tensor m in (cm2 V�1 s�1) ofNH4VO3 as a function of the charge concentration (r) in the threecartesian directions calculated with k-dependent relaxation time.

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much larger than the one for H3SVO3 and NH4VO3 systems, ascan be seen in Fig. 6.

Fig. S14 (ESI†) shows the time dependence of the electronicpopulations of the (CBM + 4) state where the electron is initiallyexcited, for H3SVO3 and NH4VO3 systems. For the sake of betterillustration, we present the sum of the two lowest energyelectron states [i.e., CBM01 = CBM + (CBM + 1)] populationsas a final state population. In order to extract the populationdecay time, the time dependence of the initial excited statepopulation and the final state population were fitted by a sumof exponential and Gaussian functions. Fig. S14 (ESI†) showsthat the initial excitation energy, DEe, is very similar for bothsystems. For NH4VO3, the initial excited state is almost com-pletely depopulated within 200 fs, and the decay time extractedfrom the fitting is 58 fs, which represents an ultrafast decayprocess of the initial excited state. It takes about 2 times longertime for the complete transfer of the population to the finalenergy state (CBM01). For H3SVO3, the complete decay of theinitially populated state (CBM + 4) takes place after 400 fs,

which is 2 times slower than in the case of NH4VO3. Also, thedecay time of the (CBM + 4) state for H3SVO3 (93 fs) is about2 times longer than for NH4VO3 (58 fs). As expected, carrierpopulation dynamics also depends on the excitation energy ascan be seen from Fig. 6 where the electron/hole relaxation timefrom different excited states is plotted for both systems. For allconsidered DEe, the electron population decay for NH4VO3

happens always faster than for H3SVO3. It is evident from theFig. 6 that except for energies DEe o 0.25 eV, the decay timeincreases slightly with increasing the excitation energy. Close tothe band edge, the relaxation process of hot electrons becomes

Fig. 6 Electron (top panel) and hole (bottom panel) relaxation times (fs)for CsVO3, H3SVO3 and NH4VO3. Electrons are excited to states with anenergy DEe above the conduction band minimum and holes are excited tostates deeper in the valence band with an energy DEh from the valenceband maximum.

Fig. 7 Nonadiabatic couplings (in meV) between states in the space of KSorbital indices for CsVO3, H3SVO3 and NH4VO3. Here j = 0 means the VBMstate.

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slower. As an example, for H3SVO3 the decay time is more than600 fs for DEe B 0.2 eV and it is only 100 fs at DEe B 0.4 eV. As amatter of comparison, previous calculations reported electronrelaxation time of 179 fs and 679 fs for FAPI and MAPIrespectively in line with the order of magnitudes reported inthe present work.48

Fig. S15 (ESI†) shows the hole population decay after initialexcitation to the excited state (VBM-2) for the considered twosystems. Similar to the case of electron population decay, thehole population decay is faster in the case of NH4VO3 comparedto H3SVO3. The energy of the initial excited hole state inNH4VO3 is a bit higher but its depopulation occurs faster thanin the case of H3SVO3. From Fig. S15 (ESI†) it is evident thathole population decay time from VBM-2 in both systems is thesame as the population decay time of VBM01 state. This issimply due to the fact that there is a direct population transferfrom VBM-2 to VBM01 without involving any intermediatestates. However, for hot electron relaxation from CBM + 4 inboth considered systems, the population time of the loweststate CBM01 is much longer than the population decay time ofthe initial states as shown in Fig. 6. This is because the decayfrom the initial state to the lower state is involving few inter-mediate states which explains the delay of the populationtransfer to the lower state after depopulating the initial excitedstate. Interestingly, polar optical (PO) phonon frequenciesresponsible of the electron–phonon scattering identified inthe previous section seems also to be responsible of the hotcarrier cooling. Energy dependent carriers thermalization processis still visible especially for H3SVO3 system (see Fig. 6). Fig. S16(ESI†) shows the phonon modes driving the hole and electronrelaxations from various high energy states for H3SVO3 withoutconvolution. It is clear from the plot that hole relaxation is drivenonly by the PO vibration mode around 85–100 cm�1, whileelectron relaxation is driven by the PO plus a contribution fromthe mode at 300 cm�1. Worth noting that this particularpolar optical phonon mode of frequency 96 cm�1 mode isalso responsible of the phonon-carrier scattering during theirdiffusion across the sample as shown in the previous section(see Table S1, ESI†).

Fig. 7 shows the nonadiabatic coupling (NAC) between statesin the valence and conduction bands for all consideredsystems. The NAC represents the carrier–phonon interaction,which allows transition between excited states in the systemand therefore drives the thermalization process of hot carriers.To our understanding such reduced thermalization process forH3SVO3 is related to the smaller NACs as compared to the onefor NH4VO3 (see Fig. 7) and also to spatial separation of chargecarriers in the case of H3SVO3 system shown earlier. Also, as ageneral trend, the cooling process of hot-carriers in H3SVO3

is slower than in CsVO3. Thus, the M-site cations play animportant role in the non-radiative cooling of photo-excitedcharge carriers. This thermalization process is driven by carrier–phonon interactions through lattice vibrations which is one ofthe main mechanisms of interband relaxation of hot carriers insemiconducting materials. The strength of these interactions isreflected in the NACs (Fig. 7).

E. Room temperatures carrierdiffusion coefficient and diffusionlength

For the practical applications of the metavanadates as photo-active absorbers, it is important to evaluate their transportproperties not only under doping, but also under charge injectionregime at operating temperature. After calculating the electricalmobility, scattering time as well as the hot carrier relaxation timein the previous sections, one could correlate all calculatedquantities to estimate the diffusion coefficients. The diffusioncoefficient is directly related to the mobility via Einstein’s

relation: D = mavekbT/e, where mave ¼neme þ nhmhne þ nh

is the mobility

calculated at similar carrier concentration for electrons andholes (ne = nh) at 300 K as reported in Table S2 (ESI†). In termsof average mobility, the hybrid materials NH4VO3 and H3SVO3

show average mobilities superior to those of their inorganiccounterpart CsVO3. Consequently, the diffusion coefficient ofNH4VO3 is one order of magnitude higher than CsVO3 whileH3SVO3 sits in between.

Quantitatively, D increases from B0.25 cm2 s�1 for CsVO3 toB0.7 for H3SVO3 and reaches up to B3.35 cm2 s�1 for NH4VO3

(see Table S3, ESI†). Worth noting, for sake of comparison, thatfor hybrid perovskite light absorbers such as MAPI, diffusioncoefficients of 1.04 cm2 s�1 for holes and 1.5 cm2 s�1 forelectrons have been reported.

Another important quantity to evaluate the quality of carriercollection in photo absorbers could be deduced from the

diffusion length LD ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDtrecð Þ

p, that represents the average

diffusion distance of the minority carriers with a specific life-time from the point of generation.49 Diffusion lengths areclosely related to the carrier collection probability and areindication of materials having longer carrier lifetimes. Forcomparison, MAPI has LD = 0.105 mm for holes and 0.129 mmfor electrons.50 The estimation of carrier lifetime requires theevaluation of the recombination time which in the case of theseindirect band gap semiconductors not straightforward. Nevertheless,we make the rough assumption that the minimum recombinationtime tmin

rec is at least equal to the longest carrier cooling time extractedfrom the previous section, namely tmin

rec = 550 fs for H3SVO3 andtmin

rec = 105 fs for NH4VO3 and CsVO3. Hence, the lower limit of

the diffusion length LminD ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDtmin

rec

� �qat 300 K is reported

in Table S4 (ESI†) for a range of injected carrier densities. Itshows that under charge injection regime (ne = nh) at roomtemperature, NH4VO3 and H3SVO3 have remarkably highdiffusion length (Lmin

D 4 0.5 mm) surpassing their inorganiccounterparts demonstrating improved photogeneration andcharge collections properties.

In summary, we demonstrated that enhanced electronictransport is obtained in the case of NH4VO3 and H3SVO3 dueto the formation of extra transport channels, created by hydro-gen bonding.

The result is mainly attributed to the formation of hydrogenbonds bridging between the VO4 chains and the organic cation

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along which electrons could be transferred thus enhancinggreatly the separation and transfer efficiencies of charge andthe electronic dimensionality of these materials. The presentconcept goes beyond the standard belief that the dimensionalityof charge carrier transport is lower or equal to the subnanometerstructural dimensionality.35 Hence cation replacement can beused as an effective tool to tune the optoelectronic properties ofhybrid materials. For example, there are already strong indicationsthat the long molecular binders used to synthesize 2D/3D, 2D and1D lead halide perovskites might play the role of carrier transportchannels.51

We show that significant enhancement of photovoltaicproperties could be achieved while using an organic M-site cationby enhancing the carrier mobility. We note also an importantincrease of the intra band relaxation time. This is not expected toimpact the performance of conventional cells, which is controlledby the carrier lifetime but could be of interest in case novel cellsenabling the collection of hot carriers.

Conclusions

We demonstrated a new concept enabling the enhancement ofthe charge carrier transport and optoelectronic properties oftransition metal oxides by incorporating hydrogen bondedmolecular cations. This was achieved by means of a coherentand complementary state-of-the-art computational investigationsupported by comparison to experimental findings. We showedthat cations forming hydrogen bonds with the inorganic frame-work can enhance the electronic dimensionality of the systemrelated to the connectivity of the atomic orbitals of the mole-cular cation to the framework and forming new inter-channelselectron and hole transport pathways. We demonstrated that forhydrogen bonded hybrid materials the electronic dimensional-ity could exceed their structural subnanometer dimensionality.This concept could be generalized to the broader family of hybridmaterials.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Computational resources are provided by research computingat Texas A&M University at Qatar. FE, SS and FA acknowledgesupport from the Qatar National Research Fund (QNRF) throughthe National Priorities Research Program (NPRP 8-090-2-047). TB,and FE would like to acknowledge fruitful discussion with AlirezaFaghaninia.

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